Mind Reader

This is a game which looks magical, but has an underlying principle that can be easily grasped. To play this you need mind reader cards.

Now ask your friend to think of a number less than sixty-three. Let him/ her say which of the cards has the number she/ he thought of. Add all the corner numbers in the card which your friend pointed out. Their sum gives the card in which the number was present. The principle is so simple that you can make your own cards which are different from these.

Procedure:

To do this first make magic tables for numbers from 1 to 9. You need 4 cards with the corner numbers 1, 2 , 4 and 8. (The bold part around 1 means it is a corner number.) You have to put all the numbers from 1 to 9 in these four cards in such a way that adding the corner numbers of the cards in which a number appears gives that number. In other words, you have to write down all the numbers from 1 to 9 as the sum of some or all of the numbers 1, 2, 4 and 8. 1 and 2 already appear in the cards. 3 can be written as 1 + 2. So it must appear in the tables with 1 and 4. 4 is already present. 5 can be written as 4 + 1. Hence it must appear in the cards with and 1 and 4. Similarly continue for all the numbers upto 9.

There is no need to start a new table for the number 10. We can express it as 8 + 2. Hence it can be fitted in the cards with 8 and 2. In this way how many numbers can you fit within the first 4 cards? If you have to make 16 this time you need another card and similarly for 32 and onwards your need may. Find out the greatest number your mind reader is capable of reading with 6 cards. (Tables with corner numbers: 1, 2, 4, 8, 16, 32)

Questions:

What is the understanding concept mind reader is working on?

How and why it works?

Now try changing the corner numbers to 1, 2, 3 and 5. Can you generate another set of tables?

One explanation of mind reader is given using base 2 numbers, can we make mind reader card using base five?